Question
Multiply polynomial $ \, \color{blue}{ x^2-6x } \, $ by $ \, \color{orangered}{ x^2-6x+4 }$.
Answer
$$ \left( \color{blue}{x^2-6x} \right) \cdot \left( \color{orangered}{x^2-6x+4} \right) = x^4-12x^3+40x^2-24x $$
Explanation
We can multiply polynomials by using a GRID METHOD
Write one of the polynomials across the top and the other down the left side.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & & & \\ \hline \color{blue}{-6x} & & & \\ \hline \end{darray} $$Fill in each empty box by multiplying the intersecting terms.
$$ \begin{darray}{|c|c|c|c|}\hline & \color{blue}{x^2} & \color{blue}{-6x} & \color{blue}{4} \\ \hline \color{blue}{x^2} & \color{orangered}{x^4} & \color{orangered}{-6x^3} & \color{orangered}{4x^2} \\ \hline \color{blue}{-6x} & \color{orangered}{-6x^3} & \color{orangered}{36x^2} & \color{orangered}{-24x} \\ \hline \end{darray} $$Combine like terms:
$$ x^4-6x^3-6x^3 + 4x^2 + 36x^2-24x = \\ x^4-12x^3+40x^2-24x $$This page was created using
Polynomial Operations Calculator